A new emission inventory was compiled for the EU-wide anthropogenic transport activities, supplemented by the anthropogenic non-transport activities. In addition to this anthropogenic emission inventory, we included various natural emission sources in the LOTOS-EUROS computations. These included sea spray aerosol emissions, and the dust emissions from road suspension, agriculture, and bare soils. These were modelled as described by Schaap et al. (2008).

The baseline emission data in the anthropogenic emission inventory contains the following substances: NOx, SO2, non-methane volatile organic compounds (NMVOC), CH4, NH3, CO, PM10, PM2.5, EC (elemental carbon), B[a]P (benzo[a]pyrene), and PN (Denier van der Gon et al., 2014). The anthropogenic PN inventory includes particles in the size range of 10–300 nm.

The emission data can be calculated for the individual countries; the official UN ISO3 Country Codes were used. We have used three groups of countries. The EU15+ group is defined to include EU15 as well as Norway and Switzerland. The EU12+ group contains the new member states, Malta and European non-EU countries; the latter refers to the other European countries in the United Nations Economic Commission for the Europe domain. The EU27+ group consists of EU15+ and EU12+. Emissions from international shipping have been estimated for the various European sea regions.

The first European particle number emission inventory was made in the EU FP6 project EUCAARI (Denier van der Gon et al., 2010a; Kulmala et al., 2011). This inventory was used as a starting point for the present study. For the different transport modes (road, rail, air, and maritime navigation), a new bottom-up PN emission estimate was made, including also technologies and activities in the future years, 2020 and 2030.

The above-mentioned PN emission inventory includes only anthropogenic sources; the emissions from mainly natural sources, such as wild land fires, windblown dust, and sea salt, are not included. The inventory also does not include vegetation-related emissions (e.g., Guenther et al., 1995), or the formation of PNCs from biogenic VOCs (volatile organic compounds) (e.g., Paasonen et al., 2012).

The above-mentioned emission inventory describes internally mixed PN emissions originating from several source categories in 12 size bins, covering the particle dry diameter range from 10 to 250 nm. The LOTOS-EUROS model in combination with the M7 module uses the PN emission as input; that is converted into the Aitken and accumulation modes used in the M7 module. The M7 module additionally requires the associated masses of black and organic carbon, sulfate and mineral dust, and a division to soluble and insoluble material. Using the sulfate content of the internally mixed particles as a proxy, the PN concentrations were attributed to the soluble and insoluble modes.

The emission inventory included exhaust emissions from vehicular traffic for the network of roads and streets in the Helsinki metropolitan area (HMA). The traffic volumes and average travel speeds of each traffic link were computed using the EMME/2 transportation planning system (INRO, 1994). Traffic volume data in 2008 was used as input for the estimation of annual average road traffic emissions in the HMA. The final emission inventory consisted of average hourly emissions for each line source over the year, separately for weekdays, Saturdays, and Sundays.

The emission factors for vehicular traffic determined by Gidhagen et al. (2005) in Stockholm have been used. They reported fleet aggregate emission factors of particle number, based on measurements of the contribution of a vehicular fleet in different urban micro-environments. These values were estimated to optimally correspond to the climatic and traffic conditions in Helsinki. These values are 2.70 × 1015 and 1.8 × 1014 particles km-1 per vehicle for heavy- and light-duty vehicles, respectively. This approach does not specify separate emission factor values for diesel and gasoline vehicles; instead such composite emission factors represent the combined emissions originating from both diesel and gasoline vehicles. These values were determined for driving speeds less than 70 km h-1; however, we have applied these values for all urban roads included in the computations. Clearly, measurements are also available for the PN emission factors, based on laboratory measurements (e.g., Giechaskiel et al., 2012). However, the values determined in laboratory studies are specific for the measured individual vehicles, driving cycles, and dilution rates.

In addition to the computations for 2008, we computed the PNCs at the roadside traffic station at Ring road 1, Malmi (called simply as “Ring road 1” in the following), in 2012, for model evaluation purposes. For the hourly computations in 2012, the 2008 traffic volume data were scaled using the ratio of the total vehicular mileage (km a-1) in the HMA in 2008 and 2012. These mileage values were obtained from the national traffic emissions data archive LIPASTO (http://lipasto.vtt.fi/en/index.htm).

The importance of the shipping emissions was evaluated based on Soares et al. (2014). They showed using the STEAM2 shipping emission modelling (Jalkanen et al., 2012; Johansson et al., 2013) that the contribution of primary shipping emissions of to the concentrations of PM2.5 are only 3 % on the average in the Helsinki metropolitan area. However, this contribution can be higher than 20 % in the vicinity of the harbours (within a distance of approximately 1 km).

Emissions from stationary sources were not included. However, major stationary sources in the area (these are mostly power plants) have previously been shown to have a negligible effect on the PM2.5 concentrations near the ground level in Helsinki (Kauhaniemi et al., 2008); the same was assumed to be valid also for PNCs. Emissions from small-scale combustion were not taken into account, as their spatial distribution was not known with sufficient accuracy. The contribution of small-scale combustion to the total PM2.5 emissions in the Helsinki metropolitan area has been estimated to be 23 % in 2009 (Malkki et al., 2010). The emissions of PM2.5 originated from aviation in the Helsinki metropolitan area were about 17 % of the total road traffic PM2.5 emissions in the area in 2008.

Emission factors for traffic exhaust (measured at an ambient temperature of +33 ∘C) were extracted from the emission database of the TRANSPHORM project (Vouitsis et al., 2014) Emission factors for PN in Oslo and in other studies (Klose et al., 2009; Olivares et al., 2007) have been found to have a significant dependence on ambient air temperature. A dependence of -3 % K-1 has been applied to the Oslo traffic emissions, leading to significantly higher emission factors in the cold winter period (approximately double) than those provided in the emissions database.

Shipping emissions were based on the STEAM2 emission model (Jalkanen et al., 2012; Johansson et al., 2013). Emissions for PN were based on the CO2 emissions, converted first back to fuel consumption, and then PN emissions were calculated using an emission factor of 1 × 1016 particles (kg fuel)-1, recommended by Petzold et al. (2010). Shipping emissions were evaluated in a domain of 29 km × 18 km and thus only included shipping in the Oslo fjord area.

Domestic heating emissions of PN, due mostly to wood burning, were calculated based on a previously compiled PM2.5 inventory. A conversion factor of 4 × 1014 particles (g PM2.5)-1 emitted was used to convert PM2.5 emissions to PN emissions, based on the data presented in Hedberg et al. (2002). Other emissions concerning combustion sources, i.e. agricultural, industrial, and mobile sources use the existing PM2.5 emissions inventory and convert to PN using a ratio similar to diesel truck emissions; a conversion factor of 3 × 1015 particles (g PM2.5)-1 was applied.

Road traffic data and road characteristics were obtained from a national database (www.nsl-monitoring.nl). Road traffic data contains information about the number of vehicles, speed, congestion, and fleet composition in-between traffic links for every major road and motorway in Rotterdam. The road characteristics refer to, e.g., the width and height of buildings along the road.

The following emission factors from COPERT IV (Gkatzoflias et al., 2012) and the TRANSPHORM database have been applied: (i) for motorway traffic, 1015 particles km-1 veh-1 for heavy- and light-duty vehicles, and 0.3 × 1015 particles km-1 veh-1 for passenger cars; and (ii) for urban road traffic, 0.5 × 1015 particles km-1 veh-1 for heavy- and light-duty vehicles and buses, and 0.3 × 1015 particles km-1 veh-1 for passenger cars.

As mentioned above, two composite emission factors were used for passenger cars, one for motorway traffic, and the other one for traffic in urban roads. This was necessary, as the available traffic flow data were also in composite form, including a value for each street for each of the following vehicle categories: passenger cars, lorries, and busses. The assumption of composite emission factors implies that the fractions of passenger cars equipped with diesel, petrol, and vehicle technologies are not spatially variable within the city. However, these composite emission factors take into account, e.g., the differences between the emission factors of cars using gasoline and diesel fuels.

Airports and refineries can be potentially important sources for PN emissions (Keuken et al., 2015a, b). However, the Airport Rotterdam is a relatively small airport; for example, the annual average number of passengers is smaller than 10 % of that of the main airport in the Netherlands, the Schiphol Airport in the vicinity of Amsterdam. Major refineries are located at a distance of 10 km west of the modelling domain. Both the emissions from the Airport Rotterdam and refineries have therefore been included in the regional background.

The road traffic data for London have been obtained from London Atmospheric Emission Inventory (LAEI; GLA, 2010). Each road link was characterised by the amount of vehicles per day per vehicle category and mean speed. The traffic activity data were disaggregated by vehicle categories such as motorcycles, cars including taxis, buses, light-goods vehicles (LGV) and heavy-goods vehicles (HGV). The HGVs are further subdivided into articulated HGVs and rigid HGVs categories. The fleet compositions have been further subdivided as per fuel type, weight, engine size, and emission standards.

The emission model in the current version of the OSCAR system commonly uses the emission functions and factors based on COPERT IV (Gkatzoflias et al., 2012) and the Department for Transport (DfT) emission data base. However, due to the unavailability of emissions in that database for PNs, emission factors from Jones and Harrison (2006) have been used in this study.

According to the LAEI (GLA, 2010), the most important source categories of PM10 in London in 2015 were road transport, agriculture-nature, and industrial processes. The PM10 emission from shipping was only 2 ton year-1, which is a negligible fraction (0.08 %) of total emissions. We therefore neglected the influence of shipping in the case of London. The contribution of mass-based particulate matter emissions originating from small-scale house heating is also negligible, compared with that of the other main source categories in London. We therefore did not include house heating as a separate source category in the urban-scale computations in London.

For Athens, PN emissions included vehicular traffic, shipping, and aviation. Emission factors for traffic exhausts were taken from the TRANSPHORM emission database (Vouitsis et al., 2014). Emissions from shipping and the major ports, and airport emissions were calculated on the basis of the operational action plan for air pollution management in Athens. This plan was developed for 2004, using activity and fuel consumption data (Samaras et al., 2012). The emission factor used for shipping was 1016 particles (kg fuel)-1 according to Petzold et al. (2010), and for aviation 6 × 1014 particles (kg fuel)-1, assuming a fuel sulfur content of 1000 ppm (Lee et al., 2010).

The chemistry-transport model LOTOS-EUROS (Schaap et al., 2008) was used in this study to evaluate the regional background PNCs. Compared with other widely used chemical-transport models in Europe, reviewed by Kukkonen et al. (2012), the model is of intermediate complexity. The relevant processes have been parameterized in such a way that the computational demands are modest. The LOTOS-EUROS model has been included in several international model inter-comparison studies that have addressed the dispersion and transformation of ozone and particulate matter (e.g., Stern et al., 2008; Solazzo et al., 2012a, b). The model performance has in these model inter-comparisons been comparable with other European chemical-transport models.

The M7 aerosol microphysics module (Vignati et al., 2004) was coupled to the LOTOS-EUROS model. This module accounts for nucleation and condensation of H2SO4, and coagulation of particles. The default nucleation scheme was replaced by the activation type parameterization of Kulmala et al. (2006), which is better suited for the boundary layer. In the model treatment, the processes of nucleation and condensation are interdependent; they are linked by the availability of H2SO4. In the M7 module, the amount of H2SO4 that is available for nucleation is limited by the amount of H2SO4 that is condensed onto existing particles, within each numerical time step.

Formation of H2SO4 was based on the default gas-phase chemistry of LOTOS-EUROS, using emission inventories provided by the MACC (Monitoring Atmospheric Composition and Climate) project (TNO-MACC emission inventory) and the TRANSPHORM emission inventories. The PN emissions were converted to values that are compatible with the M7 module, using assumptions on the chemical composition of particulate matter (cf. Sect. 2.2.1).

Although the size range of the anthropogenic emissions was assumed to be from 10 to 300 nm, the dispersion computations were performed for the size range of 10–1000 nm. There are several reasons for the relatively wider size range of the dispersion computations. First, due to condensation and coagulation, particles may grow to larger sizes than 300 nm. Second, small particles interact with larger particles (even larger than 300 nm); the latter can originate from natural sources such as sea salt. The structure of the M7 model also includes the Aitken and accumulation size modes, with no strict separation at 300 nm.

Two sets of simulations for Europe were made, for the target years of the TRANSPHORM project, viz. 2008 and 2005. (i) The first set was based on the meteorology of 2008, and was used for model evaluation. This set had a 0.5 × 0.25 longitude–latitude grid, for a European domain from 15∘ W to 35∘ E and from 35 to 70∘ N. The concentrations for particle numbers were assumed to be negligible at the boundaries of the domain. (ii) The second set of simulations was performed for the meteorology and the emissions of 2005. Additional simulations were performed for each target city, on a finer 0.125 × 0.0625 longitude–latitude grid, for each city in a domain that covered an area of 3∘ × 1.5∘, using the European-scale simulation for boundary conditions.

There are several processes that contribute to uncertainties in the model results. Nucleation mode particles contribute substantially to the total particle numbers. However, several parameterizations for nucleation processes are available, and it is not in all cases clear, which are the optimal ones. The uncertainties associated with the modelling of particle nucleation have mainly an impact on the number concentration of particles smaller than 100 nm (e.g., Fountoukis et al., 2012).

Some atmospheric species are not represented in the M7 module. For example, secondary aerosol formation from biogenic emissions (such as isoprene and terpene) is not taken into account. Riipinen et al. (2011) investigated the role of condensable vapours on the growth of freshly nucleated particles until the cloud condensation nuclei size, and proposed a semi-empirical modelling approach. Secondary organic vapours can condense on existing particles, and thus contribute to their growth. This process increases the probability of such particles to reach the sizes that are cloud condensation nuclei (CCN) active, before getting scavenged by the background particle population. Secondary organic aerosol from biogenic origin therefore may substantially contribute to the PNCs.

The emissions of condensable gases from combustion processes are also not taken into account in the modelling; these could potentially contribute, e.g., in areas with substantial residential wood burning. In regions with intensive NH3 emissions (e.g., from agriculture and animal husbandry), the impact of secondary inorganic aerosol may be significant on number and size distribution of particulate matter; this is not accounted for in the M7 module (Vignati et al., 2004).

The omission of biogenic secondary aerosol causes inaccuracies to the PM size distribution. The inaccuracies are the largest in the case of the smallest particles. The modelled sum of the Aitken and accumulation mode particle number concentrations are therefore considered the most appropriate quantity to represent regional background PNCs in this study (compared with using the number concentration of the nucleation mode particles).

For each modelling system, we address (i) the urban dispersion modelling system and its implementation, (ii) the evaluation of meteorological variables (used as input for the urban modelling), and (iii) the assessment of regional background concentrations.

The urban-scale dispersion of vehicular emissions was evaluated with the CAR-FMI (Contaminants in the Air from a Road – Finnish Meteorological Institute; Kukkonen et al., 2001; Härkönen et al., 1996) model. The model computes an hourly time-series of the pollutant dispersion from the line source. The dispersion equation for the line source model is based on a semi-analytical solution of the Gaussian diffusion equation for a finite line source. The dispersion parameters are modelled as a function of the Monin–Obukhov length, the friction velocity and the mixing height. Traffic-originating turbulence is modelled with a semi-empirical treatment.

The receptor grid intervals range from 20 m in the vicinity of major roads to 500 m on the outskirts of the area. The concentration values were computed at 18 692 receptor points.

Input data needed by the dispersion model was evaluated using a meteorological pre-processing (MPP-FMI) model that has been adapted for an urban environment (Karppinen et al., 2000). The MPP-FMI model is based on the energy budget method. The model utilises meteorological synoptic and sounding observations, and its output consists of estimates of the hourly time series of the relevant atmospheric turbulence parameters and the boundary layer height. The computation is based on a combination of the data from the stations at Helsinki-Vantaa airport and Helsinki-Kumpula (3 h synoptic weather observations), and Jokioinen (soundings).

The urban background concentrations of PN both for 2008 in 2012 were estimated to be equal to the measured hourly values at an urban background measurement site located at Kumpula in Helsinki. This station is part of the network of stations called Station for Measuring Ecosystem – Atmosphere Relations (SMEAR-III) (Järvi et al., 2009). This data contained PNCs in the particle size range from 3 to 950 nm. The measurements and data analysis were conducted according to Wiedensohler et al. (2012). Therefore, for the computations in Helsinki we did not use the regional background concentration values predicted by the LOTOS-EUROS model.

Calculations of concentrations were carried out using the EPISODE dispersion model, which is part of the integrated air quality management tool AirQUIS (Slørdal et al., 2008). The EPISODE model consists of a gridded Eulerian model coupled with a Gaussian line source model for modelling the local contribution at receptor points near roads. The Eulerian grid model uses a 1 km × 1 km grid covering Oslo. There are 13 vertical layers in the model, up to the height of 4000 m, with the lowest layer being 10 m thick. Emissions from traffic sources are placed in the lowest layer, whilst emissions from domestic heating, industry, and shipping are placed in the layers between 10 and 35 m.

Receptor points within 500 m of a road include line source calculations, using the Gaussian line source model in EPISODE; otherwise, only the Eulerian model contributes. The model coupling leads to a double counting of the emissions near roads, which has been estimated to contribute a maximum increase of 5–20 % to the model concentrations at receptor points near roads. The receptor points are placed at monitoring sites, and at aggregated home addresses, at the centre of population mass within a 100 m × 100 m grid.

The air pollution originating in vehicular traffic tunnels has been modelled assuming that there has been no deposition of particles within the tunnels. The tunnel exits are therefore treated simply as exit points of polluted air.

Meteorology is generated in the model using the diagnostic wind field model MCWIND. The MCWIND model uses meteorological measurements and interpolates these in space, adjusting for topography and atmospheric stability. Measurements from two sites are used (Valle Hovin and Blindern); both sites are centrally located in Oslo. Data required by the dispersion modelling are atmospheric stability, wind speed, and wind direction.

Hourly regional background concentrations were derived using predictions from the LOTOS-EUROS model at a number of grid squares surrounding Oslo. The hourly median concentration from these grid squares was extracted for this purpose. These values were further adjusted, based on a comparison of the predicted and observed annual mean PNC measurements at Birkenes (located about 300 km south of Oslo). This procedure resulted in a rescaling of all LOTOS-EUROS predictions by a factor of 0.75.

In Oslo, a parametrization was applied to account for deposition and coagulation processes. This was only applied in the gridded model calculations, but not in the sub-grid Gaussian modelling. This parametrization is based on calculations using the MAFOR (model for aerosol transformation and dynamics) aerosol process model for road traffic emissions (Keuken et al., 2012). First, MAFOR calculations were carried out using the complete aerosol process model description and then, for simplicity, the emissions and calculations were binned into three particle size classes. Based on these computations, deposition and coagulation rates in these three size classes were derived.

The change of the PNC in each size bin caused by coagulation was parameterized in the following simplified form: dPNCidtcoag=-PNCi2Kc,i‾, where the subscripts i and “coag” refer to the particle size class and coagulation, respectively, and Kc,i is the coagulation rate derived using the MAFOR model. Dry deposition is described as dPNCidtdepo=-PNCivd,i‾Hgrid, where νd,i is the dry deposition rate for the ith size class and Hgrid is the depth of the lowest model grid layer.

In Rotterdam, the contribution of traffic to air quality near inner-urban roads was modelled with the urban dispersion modelling system URBIS (model for local environmental assessments) (Eerens et al., 1993; Vardoulakis et al., 2003). This modelling system contains various submodules, such as a model for line sources, called the  Pluim Snelweg model, and a model for evaluating the concentrations in street canyons, called the CAR model.

Up to a distance of 500 m, contribution from motorways was modelled with the line source dispersion module, Pluim Snelweg (Wesseling et al., 2003; Beelen et al. 2010; Keuken et al., 2012). This line source model is a Gaussian plume model. The modelling also takes into account the vehicle-induced turbulence, the roughness of the terrain, the noise screens near the motorway and the atmospheric stability. The treatments of concentration time series is based on the concept of stratified meteorology. A time series of wind speeds and directions, observed at the airport of Rotterdam, are first clustered as a frequency distribution. The contributions downwind of the motorway, based on averaged emission rates, are then weighted using these frequencies; this procedure results in an estimate for the annual average concentration.

The street canyon dispersion model CAR is based on the results of wind tunnel experiments at different road types, including street canyons. The ratio of the height of the buildings and the width of the street is used to classify the type of street canyon. A source–receptor relationship has been specified as a function of the distance to the street axis for five different road types. All streets in Rotterdam have been categorized in accordance to the model classification. The model simulates only annually averaged concentrations. The model therefore requires as input values the annually averaged emission rates, and the reciprocal annual average wind speed. The annual average concentration is assumed to be inversely proportional to the wind speed. The wind speed was retrieved from measurements by the National Meteorological Institute at the airport of Rotterdam.

The contribution of shipping to the PNCs was estimated based on a predicted spatial distribution of the emissions of NOx from shipping in the Netherlands in 2007 (Snijder et al., 2012). The NOx emission map was evaluated based on computations using as input the automatic identification signals (AIS) of ships. These computations applied for operational shipping parameters, e.g., navigational status and payload, which were based on the AIS signals. The total NOx emissions were scaled to correspond to the year 2008, using the total amounts of emissions from shipping in the Netherlands in 2007 and 2008 (Denier van der Gon and Hulskotte, 2010). The spatial distribution of the emissions of NOx was subsequently converted to the emissions of PNs, based on the observations by Petzold et al. (2010). The conversion was done using the average ratio of the NOx and PN emissions in the observations of Petzold et al. (2010).

The atmospheric dispersion of shipping emissions was evaluated using the Dutch Standard Gaussian dispersion model. This model applies the same treatment of atmospheric dispersion as the Pluim Snelweg model. For simplicity, we assumed a constant stack height of 30 m and the heat content of exhausts of 1.0 MW, for all the ships within the region.

The urban background of PNCs was estimated based on the LOTOS-EUROS model, at a grid square that surrounds Rotterdam. The urban-scale modelling has a spatial resolution of 10 m × 10 m, up to a distance of 30 m from the streets, or alternatively at the housing façade along street canyons, and up to a distance of 500 m near motorways.

The OSCAR air quality assessment system (Singh et al., 2013; Sokhi et al. 2008) has been used to estimate traffic-related PNCs across London. The models within the OSCAR system consist of an emission model, meteorological pre-processing model, and a line source Gaussian dispersion model. The roadside dispersion model within OSCAR system is the CAR-FMI model. The hourly concentrations were predicted at the receptor points placed at varying distances of 10, 40, and 90 m near both sides of the roads, and 100 m apart in the outskirts.

A range of hourly meteorological parameters are needed, including wind speed, solar radiation, friction velocity, and Monin–Obukhov length. These are provided by the dedicated OSCAR meteorological pre-processor GAMMA met, described by Bualert (2002). The meteorological model employs meteorological data, such as solar radiation, roughness length, and heat flux, to estimate atmospheric stability parameters, including the Monin–Obukhov lengths and mixing heights. Data from the meteorological station at Heathrow was used as input for the model. The effects of land use characteristics on parameters such as surface roughness, Bowen ratio, albedo, and anthropogenic heat flux are taken into account. The meteorological pre-processor needs six input parameters: time, wind speed, wind direction, ambient temperature, cloud cover, and global radiation.

The regional background levels were evaluated based on the LOTOS-EUROS simulations. We used the predicted LOTOS-EUROS concentration values surrounding the city. The LOTOS-EUROS hourly values were scaled by multiplying them with the ratio of annual average measured and predicted concentrations. The measured values used for the scaling were taken from the regional background station of Harwell.

The modelling system consists of two models: (i) the meteorological model MEMO (Moussiopoulos et al., 1993), and (ii) the chemical-transport model MARS-aero (Moussiopoulos et al., 1995, 2012). The MEMO model is a three-dimensional Eulerian non-hydrostatic prognostic model. The MARS-aero model can be used to simulate the transport and transformation of gaseous pollutants and atmospheric aerosols in the lower troposphere. The system allows for a finer grid simulation to be nested inside a coarser grid.

Meteorological data were generated using the MEMO model. Initialisation and boundary conditions data for the application of the MEMO model were based on upper air soundings for selected meteorological variables (wind speed and direction, temperature); these were performed at the Athens International Airport. Annual mean concentrations were estimated on the basis of computations for eight representative days, combined with a weighting scheme. These days were selected and assigned certain weights based on a classification of synoptic meteorological conditions in the Greater Athens area for 2008 (Helmis et al., 2003; Moussiopoulos et al., 2004).

The classification was done with the application of principal component analysis on a set of six meteorological variables (namely wind speed and direction, surface pressure, mixing layer height, cloud cover, and specific humidity), and subsequently using a subtractive clustering algorithm. Using this procedure, the different synoptic weather conditions that prevailed during each day of the year were distributed into distinct groups, which correspond to certain characteristic meteorological features (Sfetsos et al., 2005; Shahgedanova et al., 1998).

The day that appeared closer to the mean of each group of synoptic meteorological conditions was considered to be a typical day representing the specific group and was simulated with MARS-aero. The weight assigned to each of the representative days was proportional to the size of the corresponding group. The application of the methodology was based on meteorological fields predicted by the WRF meteorological model (version 3.2.1, Skamarock et al., 2005), which was applied for 2008 with a horizontal grid resolution of 50 km and a temporal resolution or 3 h. The MEMO and MARS-aero models were applied in a computational domain of 50 km × 50 km, on a spatial resolution of 500 m.

Both the regional background PNCs and the concentrations of other relevant species are needed as boundary conditions for the MARS-aero calculations. A spatially uniform annually average regional PNC background of 1800 particles cm-3 was used for the boundary conditions, based on Kalivitis et al. (2008). The regional background values of all other relevant species were extracted from the LOTOS-EUROS computations, at the grid squares surrounding the city.

Total anthropogenic PN emissions in UNECE (United Nations Economic Commission for Europe) Europe were estimated using a bottom-up methodology (Denier van der Gon et al., 2014). These are presented in Fig. 2a–b, classified according to both source sector and country group. The transport sectors (i.e., road and non-road transport) contributed approximately 60 % to the total land-based PN emissions in UNECE-Europe in 2005 (Fig. 2a). The other most important sectors include industry (defined here excluding energy industries), residential combustion, fugitive emissions, and energy industries.

The PN emissions are projected to decrease in 2020 and 2030 to less than a half of their value in 2005 (Fig. 2b). International shipping was a dominating source in 2005, but its contribution is expected to substantially decline from 2005 to 2020 and 2030, mainly due to the introduction of low sulfur fuels. The contribution of shipping is more dominant in the current inventory, compared with the first European PN emission inventory made in the EU-funded project EUCAARI (Denier van der Gon et al., 2010a; Kulmala et al., 2011). Another remarkable change compared with the previous inventory is that in the new inventory, aviation is a substantially stronger source of UFPs than previously assumed. Most of these shipping and aviation particulate emissions are not solid, but semi-volatile particles, and may therefore have escaped attention in previous emission factor measurements.

The PN emission inventory includes in principle all particulate sizes. The PN emissions in two size fractions have been presented in Fig. 3a. The UFP is defined as particles smaller in diameter than 100 nm. As expected, the difference between the total PN emissions and the UFP emissions is relatively small, as the PN emissions are dominated by the smaller size fractions.

The corresponding emissions solely for the road transport sector have been presented in Fig. 3b. The PN emissions of road transport are projected to significantly decrease in time (Fig. 3b). The PN emissions due to fuel combustion in road transport and shipping are expected to significantly decrease as a consequence of motor and fuel modifications, such as low-sulfur fuels and particulate matter filters (e.g., Ristovski et al., 2006; Morawska et al., 2008; Fiebig et al., 2014). The EU 15 emissions are estimated to decline strongly in future years, due to implementation of new emission standards in road transport, and the phase-out of the older vehicles that have less stringent emission limits.

To facilitate the modelling of PN on a regional scale, the PN emissions were spatially distributed using available proxy data (Denier van der Gon et al., 2010b). Examples of such proxy data are maps of population density, road networks, shipping tracks, land use, and port capacities. The spatial distribution of the PN emissions has been presented in Fig. 4.

The estimates for PN emissions are associated with a relatively high uncertainty, compared with the emissions of the commonly regulated pollutants. This uncertainty varies substantially in terms of the different source categories. Vehicle-originated PNCs can change on a short timescale after the emissions exit the tailpipe, due to both rapid dilution and microphysical processes. The latter depend on ambient temperature and other environmental conditions, as well as on secondary particle formation. Due to such transformations, the PN concentration flux is not conserved. For some source categories, no PN emission factors were available. In such cases, the PN emission was calculated based on PM measurements and estimated particle size distributions.

For the road transport emission factors reported here, an uncertainty analysis for the particle mass-based emission has been carried out. This analysis shows an uncertainty between 10 and 20 %, depending on the quality of the country's statistics (Kioutsioukis et al., 2010). Particulate number emission factors were not included in the uncertainty evaluation of the above-mentioned study. However, it is possible also to indirectly estimate the uncertainties of the PN emissions, based on the correlations between PN emission factors derived in this study with the COPERT PM emission factors (Vouitsis et al., 2014).

Solid particles can be measured more accurately than semi-volatile ones; the emission standards for road transport are therefore currently based on the solid fraction of PN. The PN emissions are influenced by numerous factors, such as, e.g., vehicle category, PN measuring equipment, and environmental conditions. The overall uncertainty of vehicular PN emissions can therefore be evaluated to have high uncertainties: (i) 81–144 % when after-treatment device effects are not included and (ii) 144–169 % when these effects are included (UNECE, 2010).

Road transport is the most intensively studied source category for PN emissions. It can therefore be expected that the uncertainties for other source categories are at least of the same magnitude. For example, the total PN emission factor is dependent on the set-ups of the measurements. In particular, the measurement can (i) include only solid PN, or solid and volatile PN, and (ii) the lower particle size cut-off used in the measurements can vary, as this is dependent on the instrumental method. Sometimes a lower cut-off of 3 nm is used, but frequently also only PNs for sizes larger than 20 or 30 nm are reported. This definition of lower size cut-off can have substantial effects on the estimates of the total PN emissions. For a more detailed discussion of the various techniques used to measure PN, we refer to McMurry (2000) and Morawska et al. (2008).

Another important uncertainty is caused by the sulfur content in shipping fuels. It is known what the regulatory limit values for the fuel sulfur content are, and in some cases also what the average fuel sulfur content is; however, it is not commonly known what the actual values are. Therefore, for all transport modes the uncertainty is expected to be at least equal to the previously listed uncertainty estimate for road transport; this is in the range of 100–170 %.

On a regional to city-scale, Kalafut-Pettibone et al. (2011) determined average size-resolved and total number- and volume-based emission factors for combustion. They estimated that the uncertainty of the PN emission factor is approximately plus or minus 50 %. This uncertainty value is based on longer-term temporal averages.

All of the emission inventories in the target cities included vehicular traffic. However, the details of the treatments for other source categories varied substantially from city to city. The urban inventories for Helsinki, Oslo, Rotterdam and Athens included also the primary particulate matter emissions from shipping. In the case of London, the importance of shipping emissions was found to be negligible, compared with that of other urban emissions. The stationary sources were included at varying levels of detail for Helsinki, Oslo, London, and Athens. In the case of Rotterdam, the airports, refineries, and other major sources were included in the regional background. For Helsinki, the influence of shipping and major stationary sources was estimated indirectly, but the actual PN emission values for these source categories were not included in the urban emission inventory. The influence of small-scale combustion was explicitly evaluated for Oslo, and its importance was evaluated for Helsinki.

The sulfur content of vehicular motor fuel is an important factor for selecting the emission factors of PNs. There has been a decreasing trend in the fuel sulfur (S) contents in Europe. During the later part of 2000's, the S content of motor fuels was decreasing rapidly in many European countries, commonly from < 50 ppm to < 10 ppm S. One should therefore use the vehicular emission factors (EFs) that were determined for the same S content as for the target year of modelling (in this study 2008). For all the target cities, we used the best available locally applicable EFs.

For Helsinki, calculations were based on EFs by Gidhagen et al. (2005) for Stockholm. The measurements that were the basis for these EFs were made in Stockholm for heavy-duty vehicles (HDV) in 1999 and for light-duty vehicles (LDV) in 2003. Sweden introduced its Environmental Class 1 (EC1) diesel fuel in 1991, with maximum sulfur content of 10 ppm (weight). The EC1 grade reached nearly complete market coverage in Sweden already in the 1990s, due to a strongly supportive tax policy. The EFs used for Helsinki therefore refer to fuel with lower than 10 ppm sulfur content. As also Finland used the lower S content vehicular fuel in 2008, the EFs used in the manuscript are appropriate in this respect. Also in Oslo and Rotterdam both the modelled and actual S contents of the vehicular fuel were lower than 10 ppm in 2008.

For London, the emission factors from Jones and Harrison (2006) were used, which refer to the higher (< 50 ppm) fuel S, while the target year for modelling (2008) was after the transition to lower S fuel. For Athens, the situation was the opposite: EFs correspond to the lower fuel S content, whereas a higher S content fuel was actually used. The applied EFs are therefore expected to somewhat overestimate the measured concentrations in London, and underestimate those in Athens.

The most detailed emission inventory was compiled for Oslo. The proportions of total emissions in Oslo in 2008 have been presented in Fig. 5. The sector denoted “heating” includes all heating, of which domestic heating is the largest part, 95 %. Traffic exhaust emissions were responsible for about three-fourths of the total emissions; the contributions from shipping, heating, and other mobile sources are also notable.

The LOTOS-EUROS model, including the M7 module, was used together with the above-mentioned new PN emission inventory, to evaluate the PNCs in Europe.

The predicted PNCs were compared with the EUCAARI measurements (Asmi et al., 2011), with a focus on eight selected stations: Cabauw, Melpitz, Vavihill, Harwell, SMEAR, Ispra, Kosetice, and Kpuszta. Cabauw is a rural site in an agricultural area in the Netherlands, with influence from the nearby city of Rotterdam; this is the type of region for which the model is well suitable. Melpitz is a rural site in Germany, the concentrations of which are dominated by long-range transport and biogenic emissions. The site of Vavihill in Sweden is close to the sea; this site is representative for fairly clean background conditions, with occasional influence from shipping and nearby cities. The station of Harwell (UK) is a regional background site that can occasionally be influenced by the urban plumes originating in London. The SMEAR II site (in Hyytiälä, southern Finland) is a high-latitude regional station, exposed alternatively to both clean and fairly polluted air masses. The site of Ispra (Italy) is in the vicinity of the Alps; it experiences the influences of the polluted air from the Po Valley. The site of Kosetice (Czech Republic) is located in the agricultural countryside. Kpuszta represents the central European regional background, relatively far from local sources.

Modelled PNCs in the Aitken and accumulation mode were compared with the observed PNCs in size bins 30–50 nm, > 50 nm, and > 100 nm (the latter two bins are partly overlapping). Measured and modelled monthly average PNCs for the eight sites have been presented in Fig. 6a–d. The nucleation mode was excluded. The values correspond to the size fraction 30–250 nm for the observations, and the sum of Aitken and accumulation mode for the LOTOS-EUROS computations (defined as the interval 10–1000 nm).

At Vavihill, the modelled and observed monthly average concentrations match well for the whole year. At Cabauw, the observed concentrations from January to April were not measured at the ground level, but instead at a height of 60 m; these values are therefore not comparable with the predictions. Since May, the overall measured and predicted levels of the PNCs at Cabauw were fairly well in agreement. The modelled monthly average concentrations at Melpitz were clearly lower than the corresponding measured values. These relatively high measured values have probably been caused by the substantial contribution of particles formed from biogenic emissions, which were not accounted for in the present model version. In winter, when the biogenic emissions are smaller, the model and observations match relatively better at Melpitz. The predicted monthly concentrations at Harwell agree well with the measurements; the model is well suited for this type of environment. For the site of SMEAR, the model under-predicts; contributions from biogenic emissions in summer are not taken into account in the model. For the site of Ispra, the concentrations in winter were the highest observed amongst the stations considered here, and the model substantially under-predicted. This location is, together with Cabauw, most strongly affected by anthropogenic emissions. In particular in winter, high concentrations are expected due to wood burning, in combination with stagnant conditions in the Po valley. For the site of Kosetice, the model shows a smaller underestimation in winter than in summer. For K-Puszta, statistics before September are based on a small set of measurements and are therefore only indicative.

The correlation coefficients were reasonable, ranging on the average from 0.3 to 0.6 for the stations in Fig. 6c, and from 0.3 to 0.5 for the stations in Fig. 6d. A higher correlation was not always related to an accurate estimate of total particle number.

Modelled values were on the average within a factor of 2 of the measured values for the Aitken mode, compared to observed particle modes in the range 30–100 nm (results not shown here). However, the number of particles with a diameter > 100 nm was under-predicted, whereas the number of particles < 100 nm was in most cases over-predicted. Fountoukis et al. (2012) previously reported a similar result; a systematic under-prediction of the number of particles larger than 100 nm, using the original EUCAARI emission inventory and another chemical-transport model.

These model evaluation studies indicate that the applied regional-scale modelling provides reasonably accurate results for PNCs in the size range larger than 30 nm, in the presence of dominating anthropogenic emissions. In case of substantial biogenic contribution, the predicted PNCs will probably be underestimates. Clearly, the prediction of particle size distributions is a more challenging task, compared with the prediction of the PNCs integrated over all particle sizes.

The modelled European-scale PNCs for 2005 and for 2008 are presented in Fig. 7a–b. The differences of the concentrations between these two years have been presented in Fig. 7c–d.

The anthropogenic emissions of PN were assumed to be the same for these two years. However, for the emissions of gases, we used the MACC project emissions for the different years. The meteorological conditions and the natural emissions (which were influenced by meteorology) were also assumed to be different. During both years, the highest concentrations occurred at urban and industrialized areas, and along the most densely trafficked shipping lanes. Annual mean concentrations reached values of up to 10 000 cm-3 for 2005. For most regions, the PNCs were higher for 2005, compared with those for 2008.

The largest concentration differences between the two target years were approximately 25 %. The fairly large differences of the concentrations near the western boundary of the domain are caused by the natural emissions, which were determined by the meteorological conditions. At other locations, differences are due to the combined effect of meteorology and decreased SO2 emissions; the emissions were lower for 2008.

We did not include a treatment of aerosol processes to all of the urban-scale modelling systems used in this study. Instead, their influence was examined in a numerical study performed for Oslo in 2008. We have used a simplified aerosol process parametrization based on the more complex MAFOR aerosol process model and some experimental results. The numerical accuracy of the simplified model, as compared with the more complex model, was evaluated to be approximately 10 %.

The model needs as input values an initial size distribution, which was based on experimental data in Oslo, Rotterdam, and Helsinki. An initial size distribution ratio was defined as the initial fraction of the total PN concentration in each size bin (PNC1, PNC2, and PNC3). These model input values have been presented in Table 2.

The impact of this parametrisation was tested in comparison with the measured data in Oslo for a 3-monthly period from January to April, 2008. In these computations, the upper limit values were used both for the coagulation coefficient and the dry deposition velocity, in order to evaluate the maximum possible effects due to these processes.

Use of the parametrisation resulted in lower PNC levels further from sources. At the urban background station in Oslo (Sofienbergparken), the above-mentioned parametrisation resulted in a maximum reduction of PN concentrations by approximately 45 %, compared to treating PN as a tracer. The range of this percentage value, allowing for the uncertainty of the simplified aerosol process modelling, can be considered to be approximately from 40 to 50 %. The impact of deposition was larger than that caused by coagulation; however, the influences of both processes were significant. The model-derived deposition and coagulation rates in the selected three size classes and the relevant timescales are presented in Table 2.

The predicted annually averaged spatial concentration distributions in the target cities are presented in Fig. 8a–f. The same concentration legend is used for all the cities. The concentrations in various cities can therefore be inter-compared, allowing for the differences in the computational methods. The central area of London has been separately presented, by using a more closely spaced concentration legend.

The differences of the numerical results in the various cities are mainly due to the differences in the spatial distribution and strengths of emissions, the regional background contributions, meteorological conditions, and other specific characteristics of the cities. Clearly, these differences are also partly caused by the inaccuracies and deficiencies of the methods. In particular, the concentration distribution for Athens was evaluated on a spatial resolution of 500 m, which is coarser that the corresponding resolution used for the other cities; this tends to smooth out the maximum concentrations on finer spatial scales. Further, the modelling in this study did not explicitly allow for the influence of street canyons in all the target cities, except for the semi-empirical modelling of the effects of street canyons in Rotterdam. The predicted PNCs at street canyon locations, and more generally in the vicinity of locations that are influenced by high buildings tend therefore to be under-predictions in this respect.

The maximum values of annual average PNCs were approximately 20 000 in Helsinki, 30 000 in Oslo, 30 000 in Athens, and 50 000 in Rotterdam and London. These values were relatively higher in London, due mainly to very high traffic flows along the most trafficked roads, and in Rotterdam, due to both high regional background and intensive urban traffic.

The locations of harbours and airports in the target cities have been presented in Fig. A1 in Appendix A. Also tunnel entrances have been presented for Oslo. In all cities, the most important emission category that influenced the spatial distributions of PNCs was vehicular traffic; the major traffic networks are clearly visible in all the target cities. For example, the main ring road or ring roads (for Helsinki, Oslo, London and Athens) or the main highways (for Rotterdam) surrounding the city centres are clearly visible. The concentrations were also elevated in the central areas of the cities. In Helsinki, Oslo, Rotterdam, and London, the highest concentrations occurred in the vicinity of the most densely trafficked ring roads, and near the junctions of such ring roads and other major roads. In Athens, the highest predicted concentrations of PNs occurred in the vicinity of the Athens International Airport.

The second most important urban source category was shipping and harbours. Their influences on the PNCs over land areas can be distinctly detected in the case of Oslo and Athens, and to a smaller extent also in Rotterdam. In Oslo, the higher concentrations in the vicinity of the harbours are also partly caused by the traffic tunnel entrances. It was assumed that there was no deposition of particles within the tunnels; therefore, all traffic-originated PNs within the tunnels were treated as emitted at these entrances. In Athens, there were substantially elevated PNCs near the main harbour regions (Piraeus and Rafina). For Helsinki, the shipping emissions have not been included in the PNC map shown in Fig. 8a; however, it was separately evaluated that their influences can be notable near the main harbour areas (Soares et al., 2014).

In a source apportionment study for London (Beddows et al., 2015), it was shown that the urban traffic and the urban background contributed 45 and 43 %, respectively, to the total PNC at an urban background station. Further, according to the London Atmospheric Emission Inventory (GLA, 2010), shipping is responsible for a negligible fraction of the total PM mass-based emissions. We therefore conclude that considering the annual average concentration levels for the whole of London, shipping along the River Thames and the related harbour activities probably cause a small or negligible impact on the overall PNCs.

Although the harbours in the vicinity of Rotterdam are amongst the largest in Europe, the influence of harbour activities was only modestly detectable in Fig. 8c. The main reason for this was the fact that the most densely trafficked harbours in that region are located outside the city of Rotterdam. The harbours within the city of Rotterdam are located to the south and north of the river Nieuwe Maas, which flows through the centre of Rotterdam. These urban harbours serve mainly inland shipping. The larger harbours serving sea going vessels are located at a distance of 5–10 km to the west of the centre of Rotterdam, near the coast of the North Sea. The harbours within the city of Rotterdam are also dispersed on a relatively wide region on both sides of the river; this tends to spatially smooth out concentration hotspots.

A potentially important source is also vehicular traffic to the airports and aviation. In Athens, there were substantially elevated PNCs near the Athens International Airport, located to the east from the centre of the city (it is clearly visible in Fig. 8e). Detailed computations showed that aviation emissions were responsible for the largest share of the concentrations within this airport and in its immediate vicinity. The influence of the Heathrow airport in London is also visible in the PNC map (near the outer ring road on the western part of the city). However, these higher predicted concentrations were caused by the emissions from the congested roads leading to Heathrow airport. The emissions originating from aviation in London were included in the regional background concentrations (the LOTOS-EUROS predictions), but not explicitly in the urban-scale computations. The Helsinki-Vantaa airport is only slightly detectable (to the north of the outer ring road, in the northern part of the metropolitan area). The airport in Oslo is outside the modelled domain. The influence of the Rotterdam The Hague Airport is not visible; it is a fairly small airport.

There are also some other significant source categories, such as major refineries in the vicinity of Rotterdam; however, these were not located within the modelled urban domain. Especially in Oslo, the small-scale combustion in households can also be an important source in residential regions in winter.